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Sinclair was a talismanic figure during Brendan Rodgers' first spell in charge, smashing 62 goals in 167 appearances and helping deliver an historic Treble Treble.
And the former winger is adamant O'Neill remains the best choice to fend off Derek McInnes' men in the battle for Premiership glory.
Speaking to Andy's Bet Club, Sinclair said: “The criticism of Martin O'Neill? When you play against Rangers, it means so much. Playing in it, you understand how big a game it is for the fans. It's what they live for when both teams meet at the weekend.
“The main priority is to win the Premiership every season. When you're at Celtic, you're expected to play and win every single game, and it's the same with Rangers now.
“Rangers have improved but, for me, Celtic will always be the team everyone is chasing and Martin O'Neill is the right man to go and win another title.
“He has so much experience and you can see that in the way he leads Celtic to silverware. Even when fans and people are talking and aren't happy with certain results, he is still the right man to be at Celtic.
“The main thing for him is to go out and win the league, and he will do that.”
Sinclair played under Rodgers and admired Ange Postecoglou from afar, but believes a younger manager could be the way forward whenever O'Neill eventually brings the curtain down on his storied Parkhead reign.
He added: “Could Brendan Rodgers or Ange Postecoglou return to Celtic? When Martin is ready to step down, whoever goes in next, it would be exciting to have a young manager, but that's up to the board to decide.
“When you bring someone in, they have to know the club and understand the expectations that come with such a massive football club. But looking at history, Celtic usually make the right call.
“So I'm sure they'll make the right decision whenever Martin decides to step down, but that will be totally his call when that happens.”